Migration to a new Mac:
Move content to a new Mac - Apple support
Transfer to a new Mac with Migration Assistant - Apple Support
Migration Assistant 'takes over' both computers, and takes a surprisingly long elapsed time. First it may need to compute a Spotlight index of the data. Once data transfer begins, it takes a bit longer than a FULL backup, likely all afternoon to overnight. You may want to set this up late in the day and let it run overnight, and be ready for it not to be done by morning.
"the best way" is to use your Time machine backup from the old Mac as the source for Migration Assistant running on the new Mac. USB-2 is as fast as almost every Rotating Magnetic drive, and will not produce a noticeable slowdown doing this transfer.
The way that always works but will seem really slow is using Wi-Fi through your Router.
If you could use Ethernet through your Router to BOTH Macs, that would be much faster. OR, if your old Mac is running 10.12 Sierra or later it can establish an Ad-hoc private Wi-fi connection to the new Mac when placed near the new Mac and both running Migration Assistant.
If your old Mac has no Thunderbolt-3 ports, Thunderbolt Bridge is off the table.
A USB cord sounds like a great idea, but does not work because USB is a local peripheral interface, and a Network interface is required, unless you can make your old Mac ‘look like a drive' to the new Mac.
Target Disk Mode can allow your old Mac to become a Hard drive, and it can be cable-connected to the new Mac. It requires ThunderBolt cable connection, so for a Thunderbolt-2 old Mac, you would need to obtain a Thunderbolt-3 <-> ThunderBolt-2 adapter (US$50) and a Thunderbolt-2 cable.
Transfer files between two Mac computers using target disk mode - Apple Support
Transfer files between two Mac computers using target disk mode - Apple Support
